Question #81c98

1 Answer
Feb 9, 2017

Answer:

#sf(lambda=1.17xx10^(-25)color(white)(x)nm)#

Explanation:

You need to use the de Broglie expression to get an object's wavelength:

#sf(lambda=h/(mv))#

#sf(lambda)# is the wavelength

#sf(h)# is the Planck Constant = #sf(6.63xx10^(-34)color(white)(x)Js)#

#sf(m)# is the mass

#sf(v)# is the velocity

You need to get everything into standard units.

#sf(1000color(white)(x)"g"=1"kg")#

#:.##sf(m=145color(white)(x)"g"=145/1000kg=0.145color(white)(x)kg)#

#sf(60s=1"min")#

#sf(60min=1hr)#

#:.##sf(1hr=60xx60=3600s)#

#sf(1000m=1km)#

#:.##sf(v=(141,000)/(3600)=39.16color(white)(x)"m/s")#

Now put in the numbers:

#sf(lambda=(6.63xx10^(-34))/(0.145xx39.16)m)#

#sf(lambda=1.167xx10^(-34)color(white)(x)m)#

#sf(1nm=10^(-9)m)#

To convert m to nm we divide by #sf(10^(-9)rArr)#

#sf(lambda=(1.167xx10^(-34))/(10^(-9))=1.17xx10^(-25)color(white)(x)nm)#